Please help. show work.
1 answer:
17. To complete the square, add the square of half the x-coefficient.
x² -8x +4² = 9 +4²
(x -4)² = 25 = 5² . . rewrite as squares
x -4 = ±5 . . . . . . . take the square root
x = 4 ±5 . . . . . . . . add 4
The roots are x ∈ {-1, 9}.
18. The discriminant is b²-4ac. You have a=3, b=-5, c=4. So, the value of the discriminant is
(-5)² -4(3)(4) = 25 -48 = -23
The discriminant is negative, so there are no real solutions.
19. You are asked to find the positive value of t such that h(t) = 0. This is equivalent to find solutions to
-16t² +25t +3 = 0
The quadratic formula is
t = (-b ±√(b² -4ac))/(2a)
where you have a=-16, b=25, c=3. The formula gives
t = (-25 ±√(25² -4(-16)(3))/(2(-16))
t = (-25 ±√817)/-32
t ≈ 1.67447
The balloon will hit the ground after about 1.674 seconds.
20. The height at t=1 is found by substituting 1 for t in the equation for h(t).
h(1) = -16×1² +25×1 +3
h(1) = -16 +25 +3
h(1) = 12
At t=1 second, the height of the balloon is 12 ft.
x² -8x +4² = 9 +4²
(x -4)² = 25 = 5² . . rewrite as squares
x -4 = ±5 . . . . . . . take the square root
x = 4 ±5 . . . . . . . . add 4
The roots are x ∈ {-1, 9}.
18. The discriminant is b²-4ac. You have a=3, b=-5, c=4. So, the value of the discriminant is
(-5)² -4(3)(4) = 25 -48 = -23
The discriminant is negative, so there are no real solutions.
19. You are asked to find the positive value of t such that h(t) = 0. This is equivalent to find solutions to
-16t² +25t +3 = 0
The quadratic formula is
t = (-b ±√(b² -4ac))/(2a)
where you have a=-16, b=25, c=3. The formula gives
t = (-25 ±√(25² -4(-16)(3))/(2(-16))
t = (-25 ±√817)/-32
t ≈ 1.67447
The balloon will hit the ground after about 1.674 seconds.
20. The height at t=1 is found by substituting 1 for t in the equation for h(t).
h(1) = -16×1² +25×1 +3
h(1) = -16 +25 +3
h(1) = 12
At t=1 second, the height of the balloon is 12 ft.
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